The Regularity and Singularity of Solutions of Certain Elliptic Problems on Polygonal Domains

The regularity and singularity of variational solutions of problems u = f in ; @u @ T @ 2 u @ 2 = g on 1; u = 0 on 2; @u @ = 0 on 3 with suitable compatibility conditions at vertices of 1 for bounded polygonal domains R are studied by combining Grisvard's (cf. Grisvard[4]) results with perturbation theory and the method of continuity. The variational solutions are proved to be in H( ) H( 1) for certain geometric polygonal domains. The singular decomposition forms of the variational solutions are given implicitly and explicitly for other geometric polygonal domains.